(x+5y)(7x-3y)=

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Solution for (x+5y)(7x-3y)= equation: 


Simplifying
(x + 5y)(7x + -3y) = 0

Multiply (x + 5y) * (7x + -3y)
(x(7x + -3y) + 5y * (7x + -3y)) = 0
((7x * x + -3y * x) + 5y * (7x + -3y)) = 0

Reorder the terms:
((-3xy + 7x2) + 5y * (7x + -3y)) = 0
((-3xy + 7x2) + 5y * (7x + -3y)) = 0
(-3xy + 7x2 + (7x * 5y + -3y * 5y)) = 0
(-3xy + 7x2 + (35xy + -15y2)) = 0

Reorder the terms:
(-3xy + 35xy + 7x2 + -15y2) = 0

Combine like terms: -3xy + 35xy = 32xy
(32xy + 7x2 + -15y2) = 0

Solving
32xy + 7x2 + -15y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7x + -3y)(x + 5y) = 0


Subproblem 1
Set the factor '(7x + -3y)' equal to zero and attempt to solve:

Simplifying
7x + -3y = 0

Solving
7x + -3y = 0

Move all terms containing x to the left, all other terms to the right.

Add '3y' to each side of the equation.
7x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
7x + 0 = 0 + 3y
7x = 0 + 3y
Remove the zero:
7x = 3y

Divide each side by '7'.
x = 0.4285714286y

Simplifying
x = 0.4285714286y

Subproblem 2
Set the factor '(x + 5y)' equal to zero and attempt to solve:

Simplifying
x + 5y = 0

Solving
x + 5y = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5y' to each side of the equation.
x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
x + 0 = 0 + -5y
x = 0 + -5y
Remove the zero:
x = -5y

Simplifying
x = -5y
Solution
x = {0.4285714286y, -5y}

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